What is the expression for system function in z-domain?(a) \(\frac{2}{T}[\frac{1+z^{-1}}{1-z^1}]\)(b) \(\frac{2}{T}[\frac{1+z^{-1}}{1-z^1}]\)(c) \(\frac{T}{2}[\frac{1+z^{-1}}{1-z^1}]\)(d) \(\frac{T}{2}[\frac{1-z^{-1}}{1+z^{-1}}]\)I got this question in a job interview.My enquiry is from Bilinear Transformations topic in division Digital Filters Design of Digital Signal Processing

What is the expression for system function in z-domain?(a) \(\frac{2}{

1.	What is the expression for system function in z-domain?(a) \(\frac{2}{T}[\frac{1+z^{-1}}{1-z^1}]\)(b) \(\frac{2}{T}[\frac{1+z^{-1}}{1-z^1}]\)(c) \(\frac{T}{2}[\frac{1+z^{-1}}{1-z^1}]\)(d) \(\frac{T}{2}[\frac{1-z^{-1}}{1+z^{-1}}]\)I got this question in a job interview.My enquiry is from Bilinear Transformations topic in division Digital Filters Design of Digital Signal Processing
Answer» The CORRECT answer is (c) \(\frac{T}{2}[\frac{1+z^{-1}}{1-z^1}]\) Explanation: We know that y(n)-y(n-1)= \([\frac{x(n)+x(n-1)}{2}]T\) Taking z-transform of the above EQUATION gives =>Y(z)[1-z^-1]=([1+z^-1]/2).TX(z) =>H(z)=Y(z)/X(z)=\(\frac{T}{2}[\frac{1+z^{-1}}{1-z^1}]\).

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